Two functions, y = |x - 3| and 3x + 3y = 27, are graphed on thesame set of axes. Which statement is true about the solution to the
system of equations?
(1) (3,0) is the solution to the system because it satisfies the equation
y = |x - 3|.
(2) (9,0) is the solution to the system because it satisfies the equation
3x + 3y = 27.
(3) (6,3) is the solution to the system because it satisfies both equations.
(4) (3,0), (9,0), and (6,3) are the solutions to the system of equations
because they all satisfy at least one of the equations.
Answers
3x + 3y = 27
3x + 3|x - 3| = 27
3x + 3|x - 3| = ±27
3x + 3|x - 3| = 27 or 3x + 3|x - 3| = -27
3x + 3(x - 3) = 27 or 3x + 3(x - 3) = -27
3x + 3(x) - 3(3) = 27 or 3x + 3(x) - 3(3) = -27
3x + 3x - 9 = 27 or 3x + 3x - 9 = -27
6x - 9 = 27 or 6x - 9 = -27
+ 9 + 9 + 9 + 9
6x = 36 or 6x = -18
6 6 6 6
x = 6 or x = -3
y = |x - 3| or y = |x - 3|
y = |6 - 3| or y = |-3 - 3|
y = |3| or y = |-6|
y = 3 or y = 6
(x, y) = (6, 3) or (x, y) = (-3, 6)
The two systems of equations of the graph is only equal to (6, 3). It is not equal to (-3, 6) because one of the systems of equations - y = |x - 3| - only has one solution to the function. So the answer to the problem is 3 - (6, 3) is the solution to the system because it satisfies both equations.
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Answer:
y=2x+4
Step-by-step explanation:
the y-intercept is the y value of the point given. in the slope form, 2 would be your m
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Answers
5/7 = 20/28
1/4 = 7/28
20/28 + 7/28 = 27/28
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2(1+4n)+10(n-7)=2n-n
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Answers
Answer:
The function f(x) has the greatest y-intercept. Option 1 is correct.
Step-by-step explanation:
The first function is
Substitute x=0 in the given function, to find the y-intercept.
The y-intercept of f(x) is 5.
From the given graph it is clear that the y-intercept of g(x) is 2.
The third function is
Substitute x=0 in the given function, to find the y-intercept.
The y-intercept of h(x) is -2.
Therefore the function f(x) has the greatest y-intercept. Option 1 is correct.
Final answer:
The greatest y-intercept in a function refers to the function that intersects the y-axis at the highest point. We can determine this by checking the 'b' term in the equation y = mx + b.
Explanation:
To determine which function has the greatest y-intercept, you would need to examine the 'b' term in the equation y = mx + b, which represents the y-intercept. This is the point where the function intersects the y-axis. In other words, it's the y-value where the function begins. For example, within the information provided, 'ŷ-266.8863 + 0.1656x' seems to have the largest y-intercept at 266.8863.
Now consider having graphs of multiple functions; the one that intersects the y-axis at the highest point (the largest y-value) has the greatest y-intercept.
For straight lines, their slope remains the same along the line (as demonstrated in the mention of 'Figure A1 Slope and the Algebra of Straight Lines'). It's the y-intercept that determines where on the y-axis the line begins, helping us distinguish one line from another if their slopes are identical.
Learn more about y-intercept here:
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